Bayesian Quadrature Optimization for Probability Threshold Robustness Measure.

Area of Science:

• Engineering and Applied Sciences
• Computer Science
• Statistics

Background:

• Product development involves balancing controllable design parameters with uncontrollable environmental parameters.
• Ensuring product performance under varying environmental conditions is a key challenge.
• Optimizing design parameters to maximize performance probability requires robust methods.

Purpose of the Study:

• To formulate product development problems with environmental variations as active learning (AL) problems.
• To propose efficient AL algorithms with guaranteed performance for optimizing product design.
• To enhance probabilistic threshold robustness (PTR) through advanced modeling and optimization techniques.

Main Methods:

• Utilized Gaussian process (GP) models as surrogate models for the product development process.
• Formulated AL problems as Bayesian quadrature optimization for probabilistic threshold robustness (PTR).
• Derived credible intervals for the PTR measure and developed AL algorithms for optimization and level set estimation.

Main Results:

• Proposed efficient active learning algorithms with theoretically guaranteed performance.
• Demonstrated the effectiveness of the algorithms in both synthetic and real-world product development scenarios.
• Established theoretical properties of the developed AL algorithms for PTR optimization.

Conclusions:

• The developed active learning framework effectively addresses product development challenges posed by environmental variations.
• Gaussian process-based Bayesian quadrature optimization provides a robust approach to maximizing performance probability.
• The proposed algorithms offer efficient and theoretically sound solutions for optimizing probabilistic threshold robustness.